At Constant volume, the heat required to raise the temperature of 4.48 ~L of an ideal gas at STP by 15^ C is 12.0 calories. The C_p of the gas is _____________ ( R =2 ~Cal ~kg ⁻¹ ~mol ⁻¹)

Step-by-step solution

At STP, the volume of 1 mole of an ideal gas is 22.4 L . The number of moles n in 4.48 L is given by n = 4.48 22.4 = 0.2 mol . The heat required at constant volume is given by q_v = n C_v T . Given q_v = 12 cal , n = 0.2 mol , and T = 15^ C , we have 12 = 0.2 C_v 15 . 12 = 3 C_v C_v = 4 cal mol ⁻¹ K ⁻¹ . Using the relation C_p - C_v = R , where R = 2 cal mol ⁻¹ K ⁻¹ : C_p = C_v + R = 4 + 2 = 6 cal mol ⁻¹ K ⁻¹ . Answer: 6 cal